Topological Orbital Hall Effect

The orbital Hall effect (OHE) is attracting recent interest due to its fundamental science implications and potential applications in orbitronics and spintronics. Unlike the spin Hall effect, the connection between the OHE and band topology is not well understood. Here we present a novel approach for understanding the OHE based on analyzing the projected orbital angular momentum (POAM) spectrum. By considering monolayers of group IV elements, we demonstrate that the Wannier charge centers of the POAM spectrum display topologically nontrivial windings. The orbital Hall conductivity is found to form a plateau within the band gap as a direct consequence of the Chern number carried by the POAM spectrum. The topological orbital Hall phase is shown to yield a new form of bulk-boundary correspondence, which features gapless states in the POAM spectrum and induces nonzero orbital textures at the boundaries that should be amenable to experimental verification through ARPES measurements. Our study presents a systematic method for investigating the topological OHE and provides a pathway for its broader exploration in two-dimensional materials.